Acceptance SamplingProf G R C Nair

Statistical Sampling for Quality ControlAcceptance Sampling is sampling to accept or reject the immediate lot or batch of product at hand / material received. Based on the sample, a decision will be taken to accept it or reject it or in border cases, to take one more sample to enable arriving at correct decision.Prof G R C Nair

Acceptance SamplingPurposesDetermine quality levelEnsure quality is within predetermined levelAdvantagesEconomyLess handling damageFewer inspectorsUpgrading of the inspection jobApplicability to destructive testingEntire lot rejection (motivation for improvement) Prof G R C Nair

Acceptance Sampling (Continued)DisadvantagesProducers risk (Type I error- Risk of rejecting good lots ) and Consumers risk (Type II error- Risk of accepting bad lots).Added planning and documentation.Sample provides less information than 100-percent inspection.Prof G R C Nair

Acceptance SamplingLot received for inspectionSample selected and analyzedResults compared with acceptance criteriaAccept the lotSend to production or to customerReject the lotDecide on dispositionProf G R C Nair

Pros and Cons of Acceptance SamplingArguments for:Provides an assessment of riskInexpensive and suited for destructive testingRequires less time than other approachesRequires less handlingReduces inspector fatigueArguments against:Does not make sense for stable processesOnly detects poor quality; does not help to prevent itIs non-value-addedDoes not help suppliers improveProf G R C Nair

Single Sampling PlanDetermine (1) the sample size, n, and (2) the acceptance number c from tables.( the maximum number of defective items, that can be permitted to be in the sample for acceptance of the sample ) ProcedureTake one sample of size n and inspect.If the number of defective x is < c, the lot is accepted. Else (x>c),reject the lot.Prof G R C Nair

Double sampling PlanDetermine (1) the first sample size, n1(2) acceptance number for first sample,A1(3) rejection number for first sample,R1(4) second sample size , n2(5) acceptance number for second sample,A2From the tablesProf G R C Nair

ProcedureTake one sample of size n1 and inspectIf number of defective x1 is < A1,accept the lot. If x1 is > R1, reject the lot.If x1 is > A1 & < R1,take second sample of n2 andinspect. In the total, n1+n2 ,If total number of defective x1+ x2 is < A2,accept the lot. Else, reject the lotDouble sampling Plan(Contd)Prof G R C Nair

Sequential / Multiple sampling planSame logic extended. More than 2 samples are taken, in border cases.Process continued, if necessary, until a clear decision is possible

Prof G R C Nair

Example: N= 4000,max 10% defective acceptableProf G R C Nair

Sample Sample sizeCum SampleAccept NumberRejection Number1n1=2020A1= 0(0%)R1 = 4(20%)2n2=2040A2 =1(2.5%)R2 = 6(15%)3n3=2060A3 =3(5%)R3 = 8(13%)4n4=2080A4=5(6.25%) R4 = 10(12.5%)5 etc

O.C curve for any sampling plan shows the probability of acceptance of various lots with different percentage of defectives in it.Eg: OC curve for n = 100, c = 2 (max 2% defective acceptable ) sampling plan will show the probability of acceptance of lots having 1%, 2%,3%, 4% etc defectives actually getting accepted when subjected to this sort of sampling.Ideally, lots with < 2% defectives should have probability of acceptance of 1 and for lots with > 2% probability should be zero.O.C CurveProf G R C Nair

1 Ideal.9 = 0.05.8.7.6.5.4.3.2.1 = 0.1AQLLTPD 0% 1% 2%3%4%5%6%7%Prof G R C Nair

Ideal OC is only for 100% inspection.All sampling will have some sampling error.OC curves available* for various sampling plans, (or assume Poisson distribution and make).Based on the acceptable quality level (AQL), producers risk () , unacceptable quality level ( LTPD) and consumers risk (), sampling plan is chosen, balancing risk and cost. Here, AQL = 2%, = 0.05, LTPD = 5% and = 0.1Designing the sampling plan Prof G R C Nair

Acceptance Sampling--Single Sampling PlanA simple goal Determine (1) how many units, n, to sample from a lot of size N and(2) the maximum number of defective items, c, that can be found in the sample before the lot is rejected.Prof G R C Nair

Designing the PlanAcceptable Quality Level (AQL) = Max. acceptable percentage of defectives defined by producer. (Producers risk) = The probability of rejecting a good lot.Limiting Quality Level (LQL) = Lot Tolerance Percent Defective (LTPD) = Percentage of defectives that defines consumers rejection point. (Consumers risk) =The probability of accepting a bad lot.Prof G R C Nair

Operating Characteristic CurveProf G R C Nair

*3*4*5**7*Eg:- Best of five games *R1 = 20%, R2 =15% R3 =13.3% , R4 = 12.5% etcA1 = 0%, A2 = 2.5%, A3 = 5%, A4 = 6.255 . Both tend towards 10%**Eg; Thorndike Chart